revenue = price * copies
profit = revenue - cost, so
y = pq - 4q
= (240000-15000p)(p-4)
= 15000(16-p)(p-4)
= 15000(-p^2+20p-64)
That's just a parabola with vertex at p=10.
Hercules Films is deciding on the price of the video release of its film Bride of the Son of Frankenstein. Marketing estimates that at a price of p dollars, it can sell
q = 240,000 − 15,000p
copies, but each copy costs $4 to make. What price will give the greatest profit?
1 answer